The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one.…
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We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market inc…
This paper solves hedging in incomplete markets using neural networks.
problem Hedging in incomplete markets with risk factor, illiquidity, and discrete transaction dates.
method Proposes a jump-diffusion model and uses RNN, LSTM, and Mogrifier-LSTM neural networks for hedging strategies.
result Mogrifier-LSTM is the fastest and most effective model for hedging.
The paper extends cost-efficiency analysis to incomplete markets.
problem Cost-efficiency in incomplete financial markets.
method Extends results from complete markets to incomplete markets, introduces new preferences.
result Optimal portfolios in non-decreasing preferences are perfectly cost-efficient.
Solves ambiguity in incomplete markets by minimizing price measure entropy.
problem Ambiguity in pricing incomplete markets.
method Minimizes the entropy of the price measure from the economic measure, subject to mark-to-market constraints.
result Resolves ambiguity and provides a consistent pricing measure.
We show that when the price process represents a fully incomplete market, the optimal super-replication of any Markovian claim with being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of …
Study optimal investment and consumption in incomplete markets with nonlinear expectations.
problem Utility maximization in incomplete markets with general constraints.
method Utilizes -martingale method to solve optimization problem for various utility functions.
result Characterizes optimal investment-consumption strategy through quadratic BSDE solutions.
In order to find a way of measuring the degree of incompleteness of an incomplete financial market, the rank of the vector price process of the traded assets and the dimension of the associated acceptance set are introduced. We show that they are equal and state a variety of consequences.
Abstract and counterexamples show limitations of cost-efficiency in incomplete markets.
problem Understanding cost-efficiency in incomplete financial markets.
method Simple 3-state model and expected utility maximization problem.
result Characterization of perfectly cost-efficient claims and its application to incomplete markets.
Study finds optimal retirement timing in uncertain wage scenarios.
problem Optimal retirement timing in presence of uncertain wages.
method Formulated as a free boundary problem in an incomplete market.
result Developed a method to determine optimal retirement timing.
This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.
problem Quantifying convexities in incomplete markets and adjusting prices for risk and incompleteness.
method Using entropy, the essay quantifies convexities and adjusts prices for risk and incompleteness in incomplete markets.
result A new price principle derived from a log-martingale condition is introduced, matching risk aversion and adjusting for market incompleteness and default risk.
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. We provide two families of fully incomplete models: stochast…
Deep learning improves option pricing in incomplete markets.
problem Optimal pricing and hedging in incomplete jump diffusion markets.
method Stackelberg game approach, deep learning (feedforward and LSTM networks).
result Deep learning algorithm outperforms traditional methods in incomplete markets.
We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for existence and uniqueness of the solution and give a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustra…
Optimal hedging strategy found in markets with incomplete pricing kernels.
problem Finding optimal hedging in markets with incomplete pricing kernels.
method Demonstrated existence of an optimal hedge portfolio using an expected least squared-error criterion.
result Existence of an optimal hedge portfolio in Lévy-Ito markets.
The paper addresses how to complete incomplete risk markets by iteratively enhancing welfare.
problem How to complete incomplete risk markets to enhance welfare.
method Iterative mechanism to complete the market while monotonically enhancing welfare.
result Iterative completion of incomplete risk markets can enhance welfare.
The paper analyzes how wealth affects investment strategies in incomplete markets.
problem Investment strategies in markets with incomplete information.
method Developed a five-component decomposition for optimal portfolio choice, solved explicitly for HARA utility and nonrandom interest rate, and used a stochastic volatility model for US equity data.
result Demonstrated the impacts of wealth-dependent utilities on optimal portfolio allocation, including cycle-dependence and hysteresis effect.
Develops a statistical model for SOFR term structure in incomplete markets.
problem Incomplete liquidity and completeness in SOFR derivatives market.
method Statistical model incorporating macroeconomic factors and jumps in SOFR rates.
result Model is well-suited for risk management and derivatives pricing.
Method determines asset prices in incomplete markets to optimize portfolios.
problem Optimizing portfolios in incomplete markets with price constraints.
method Maximum entropy in the mean to adjust distortion function from bid-ask data.
result Prices of assets comply with portfolio optimization constraints.
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization allows us to derive the monotonicity and concavity of the optimal consumption as a…
Option Pricing Model for Incomplete Marketcond-mat.stat-mech
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option p…
We derive asset pricing formula for markets with incomplete information and subjective views.
problem Asset pricing in markets with informational imperfections and subjective investor beliefs.
method Closed-form market equilibrium formula based on Merton's model, non-linear system of equations, conditional posterior distribution.
result Derivation of market reference model for excess returns under random shadow-costs.
Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
The paper finds optimal strategies for hedging in incomplete markets using derivatives.
problem Optimal static hedging in incomplete markets with two underlying assets and vanilla options.
method Formulated as a utility maximization problem, solved through variational methods and fixed point analysis.
result Semi-analytical solutions for exponential, power/logarithmic, and quadratic utilities, with convergence to a fixed point for exponential utility.
Optimal portfolio under ratio-type periodic evaluation in incomplete markets with stochastic factorsq-fin.PM
This paper optimizes portfolio management in incomplete markets with stochastic factors, considering periodic wealth evaluations.
problem Optimizing portfolio performance in an incomplete market model with stochastic factors and periodic wealth evaluations.
method Developed a martingale duality approach to find optimal portfolio processes and dual minimizers.
result Established the existence of optimal portfolio processes and identified dual minimizers as the 'least favorable' market completion.
Hedging the Singularityq-fin.GN
AI stocks hedge against AI singularity's economic impact.
problem AI singularity's displacement of consumption.
method Developed an asset pricing model with incomplete markets.
result AI stocks command a premium due to market incompleteness.
Investor finds a fair outcome in complex financial markets.
problem Finding a fair outcome in complex financial markets.
method Recalled and proved the existence of personal equilibrium in a multistep, generically incomplete financial market model.
result Personal equilibrium exists in a multistep, generically incomplete financial market model under appropriate assumptions.
We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modeling the convergence of the buyer's and of th…
Optimal consumption and portfolio selection with Epstein-Zin utility under general constraintsq-fin.MF
Investigates optimal consumption and investment strategies with constraints in incomplete markets.
problem Optimal consumption and investment under constraints in incomplete markets.
method Characterizes optimal strategies via a quadratic BSDE, using martingale optimality criterion and Lyapunov functions.
result Obtains the verification theorem for optimal strategies in unbounded cases.
The paper challenges the assumption of a unique global time in financial markets, highlighting market incompleteness.
problem The assumption of a unique global time in financial markets is challenged.
method The paper contrasts event-time, renewal, point-process, and order-flow descriptions of financial markets.
result Non-uniqueness of time leads to a more foundational form of market incompleteness.
The paper analyzes trading strategies in a competitive market with incomplete information.
problem Strategic trading under uncertainty when firms lack full knowledge of competitors' strategies.
method Bayesian games framework to incorporate uncertainty and derive optimal trading strategies.
result Uncertainty significantly impacts trading strategies compared to complete information scenarios.
Marketron Through the Looking Glass: From Equity Dynamics to Option Pricing in Incomplete Marketsq-fin.PR
Marketron model extended to option markets, solving incomplete market challenges.
problem Tackling the challenge of incomplete markets in option pricing.
method Utility-based pricing approach, dual solution of optimal investment problem, Hamilton-Jacobi-Bellman (HJB) equation, novel calibration method.
result The Marketron model calibrated to option markets can reproduce statistical properties of underlying asset's log-returns.
We provide easily verifiable conditions for the well-posedness of the optimal investment problem for a behavioral investor in an incomplete discrete-time multiperiod financial market model, for the first time in the literature. Under two different sets of assumptions we also establish the existence of optimal strategie…
Paper uses deep learning to price and hedge options in incomplete markets.
problem Incomplete markets lack unique no-arbitrage solutions for pricing and hedging European options.
method Constrained deep learning approach with a single neural network representing option prices and hedging strategies.
result Constrained networks produce superior P&L distributions compared to unconstrained networks.
New risk measures for incomplete markets without lattice structures.
problem Risk measures on incomplete markets without lattice structures.
method Study of risk measures without lattice structures, focusing on tractable dual representations and solid superspaces.
result Existence of a tractable dual representation equivalent to a Fatou-like property, and extension theorems under certain conditions.
A pricing principle is introduced for non-attainable claims in incomplete markets.
problem Pricing non-attainable contingent claims in incomplete markets.
method Distorted Radon-Nikodym derivative and Tsallis relative entropy over a family of equivalent martingale measures.
result The pricing principle is closely related to backward stochastic differential equations and is arbitrage-free and time-consistent.
Recently, incomplete-market techniques have been used to develop a model applicable to credit default swaps (CDSs) with results obtained that are quite different from those obtained using the market-standard model. This article makes use of the new incomplete-market model to further study CDS hedging and extends the mo…
The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump…
We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market consists of a traded annuity, and, along with unspanned income, the market is incomplete. Set in a Bro…
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
This paper optimizes tracking portfolios in incomplete markets using reinforcement learning.
problem Optimizing tracking portfolios in incomplete markets with capital injection.
method Reinforcement learning approach for optimal control in reflected diffusion processes.
result Satisfactory performance of the q-learning algorithm in numerical examples.
In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, resp…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility. Our approach is based on martingale methods which rely on recent results on the e…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income …
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model parameters that correspond to the market price of the option being hedged. The second …
We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for the portfolio compressi…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases …
In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward …